Question

At 12°C and 756 mm atmospheric pressure, a balloon contains 450 ml air. If the balloon is shifted to a place of temperature 5°C and atmospheric pressure 765 mm, then indicate the nature (shape) and degree (volume) of change of the balloon.

• A. Increase in shape by a volume of 16.22 ml
• B. Decrease in shape by a volume of 16.22 ml
• C. Decrease in shape by a volume of 450 ml
• D. Increase in shape by a volume of 883.78 ml

Hint:

To calculate volume changes due to changes in pressure and temperature, use the combined gas law to adjust for both conditions simultaneously.

Answer 1

The Correct Option is A

The balloon is subject to a change in both temperature and pressure. To solve this, we use the combined gas law: \[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \] Where: \( P_1 = 756 \) mm, \( V_1 = 450 \) ml, \( T_1 = 12^\circ C = 285 \, \text{K} \) \( P_2 = 765 \) mm, \( T_2 = 5^\circ C = 278 \, \text{K} \) Rearranging the equation to solve for \( V_2 \): \[ V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} \] Substituting the values: \[ V_2 = 450 \times \frac{756}{765} \times \frac{278}{285} = 450 \times 0.988 \times 0.976 = 450 \times 0.964 = 433.8 \, \text{ml} \] The change in volume is: \[ \Delta V = V_2 - V_1 = 433.8 - 450 = -16.22 \, \text{ml} \] Thus, the volume decreases by 16.22 ml.